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A Polynomial Rate of Asymptotic Regularity for Compositions of Projections in Hilbert Space

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Abstract

This paper provides an explicit polynomial rate of asymptotic regularity for (in general inconsistent) feasibility problems in Hilbert space. In particular, we give a quantitative version of Bauschke’s solution of the zero displacement problem as well as of various generalizations of this problem. The results in this paper have been obtained by applying a general proof-theoretic method for the extraction of effective bounds from proofs due to the author (‘proof mining’) to Bauschke’s proof.

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Authors and Affiliations

  1. Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289, Darmstadt, Germany

    Ulrich Kohlenbach

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  1. Ulrich Kohlenbach
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Correspondence to Ulrich Kohlenbach.

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Communicated by James Renega.

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Kohlenbach, U. A Polynomial Rate of Asymptotic Regularity for Compositions of Projections in Hilbert Space. Found Comput Math 19, 83–99 (2019). https://doi.org/10.1007/s10208-018-9377-0

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  • DOI: https://doi.org/10.1007/s10208-018-9377-0

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